Consider the compound interest in the following cases:

(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500

(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434.

Choose the correct statement(s):

For statement (A), the given information is:

Principal (P) = Rs 16,000

Rate = 20% per annum

Time = 9 months

Compounded quarterly

When compounded quarterly, the year is divided into 4 quarters. Each quarter is 3 months, so 9 months = 3 quarters.

Rate per quarter = $\dfrac{20\%}{4} = 5\%$ per quarter

Using the compound interest formula with $n = 3$ quarters:

Amount $= P(1 + \dfrac{r}{100})^n$

Amount $= 16000(1 + \dfrac{5}{100})^3$

Amount $= 16000(1.05)^3$

Calculating $(1.05)^3$:

$1.05 \times 1.05 = 1.1025$

$1.1025 \times 1.05 = 1.157625$

Amount $= 16000 \times 1.157625$

Amount $= 18,522$

Compound Interest $= 18,522 - 16,000 = 2,522$

The statement claims CI = Rs 2,500, but the actual CI = Rs 2,522.

Statement (A) is incorrect.

---

For statement (B), the given information is:

Principal (P) = Rs 2,800

Rate = 10% per annum

Time = 18 months = 1.5 years

When compounding frequency is not mentioned, annual compounding is assumed.

Using the compound interest formula with $n = 1.5$ years:

Amount $= P(1 + \dfrac{r}{100})^n$

Amount $= 2800(1 + \dfrac{10}{100})^{1.5}$

Amount $= 2800(1.1)^{1.5}$

Calculating $(1.1)^{1.5}$:

$(1.1)^{1.5} = (1.1)^1 \times (1.1)^{0.5}$

$(1.1)^{1.5} = 1.1 \times \sqrt{1.1}$

$(1.1)^{1.5} \approx 1.1 \times 1.0488 \approx 1.15469$

Amount $= 2800 \times 1.15469$

Amount $\approx 3,233.13$

Compound Interest $= 3,233.13 - 2,800$

Compound Interest $\approx 433.13 \approx 434$

The statement claims CI = Rs 434, which matches the calculated value.

Statement (B) is correct.

---

Only statement (B) is correct.

Answer: Option 2 (Only B)